9 Answers
9

Giving an Answer closes, or ends, its three–part discussion. Unless this is a Jeopardy! episode or the like, the Answer is preceeded by

Wait for response, And open it goes.

A Question, which — unless it is phrased rhetorically — awaits a response and thus opens the discussion in a figurative sense.

Words I have three, And everyone knows me.

Question And Answer
This is rather obtuse, and that's why I never wanted to proffer this prior.

Though abstract, I am,

Such a Discussion, if it is done vocally, involves speech. Speech, as a word, refers to both an utterance of phonemes and the meaning attached to them.

Anyone can use me,

Speech is the concept abstracted of active methods and not a countable or particular thing.

I may be abstract, but some theories say I am both abstract and a type of waves.

Sound waves.

I submit a different answer here because this one, although similar (parallel?) to the train of my first, proceeds from a very different premise. Also, I'm really fond of the ‘vocal cords’ one; to be frank, I must also note that Communication et al can occur through media other than vocal speech.

$\begingroup$there is no single "I" that matches everything. "Question And Answer" has 3 words and is, I suppose, abstract; but you are not giving someone a "Question and Answer" to close the discussion - you're giving an answer - nor is Q&A a type of waves. "Sound" is both abstract and a wave, and was referenced by OP as being "correct", but "sound" is not an answer to the first 3 clues at all. With some ugly stretching you can argue that this answer is the closest fit for the question, but honestly there is no single answer that fits all the clues.$\endgroup$
– Rubio♦Oct 11 '16 at 17:48

$\begingroup$Seems like it is something related to human interaction or communication, from the hint my first guess was 'Audio Cassette Tape' - Abstract, Opens & Three words :)$\endgroup$
– WeShallSep 27 '16 at 23:56

vocal cords in the larynx, and the speech uttered thereby
> previously: speech

Give me to someone, And I am closed,

When you speak, the vocal cords tighten or ‘close’ together so as to obstruct the airways.
> previously: Here I take the use of ‘to close’ as being the malappropriated synonym for ‘to shut’, and by relation, ‘to end’. A conversation is arguably ended when someone speaks,

Wait for response, And open it goes.

When you cease speaking, the vocal cords relax and open the airway.
> previously: until, that is, another person replies. Vis à vis having the final word, et al.

Words I have three, And everyone knows me.

Granted that for this one I needed to refer to a website, but this Wikipedia page gave three colloquial names for the things: vocal folds, vocal cords, and voice reeds.
> previously: “I am ‹name›.” q.e.d.

Though abstract, I am,

Speech is both an utterance of phonemes and the meaning attached to them? That's one aspect of the concept of abstractness.

If you agree,

(Forgive me for being so arrogant.)
Alas, I would've phrased this differently, but I suppose you included the first line as rhetoric, and not as a condition for the sursequent statement:

Anyone can use me,

Not a political affirmation, but because speech is something which can be done by anyone able to do so, in that it is abstract and not a countable or particular thing.

I may be abstract, but some theories say I am both abstract and a type of waves.

Sound waves?
This is the best of my other two considerations, being ‘name’ and ‘hand’. Honestly, if it weren't for this hint which you included, I would've chosen ‘hand’.

Because the new answer was almost the same as the previous, I chose to edit rather than make a new one.

Give me to someone,And I am closed,Wait for response,And open it goes.

This refers to the sequence of using the two-way radio:
1. You need another two-way radio user to talk.
2. A two-way radio is always closed if you doesn't use it at all.
3. You can receive signal from the frequency that you had set-up, only if you are not opening the talking button.
4. As the talking button is pressed, you can talk to anyone on the same frequency.

Words I have three,And everyone knows me.

Everyone knows about radio, but when it comes to the word, we may refer it as a radio receiver or an antenna.

Though abstract, I am,If you agree,Anyone can use me,

When it comes to the radio wave itself, it is either abstract or technical that people might not really understand.
However, we use it everyday on radio receivers, and devices like walkie-talkie or smartphones also included.